# Mediation analysis using binary IV and difference scores

I have one IV ($A$) and two DVs ($B$,$C$). $A$ is a binary, experimentally manipulated variable. Each subject has two scores on $B$ and two scores on $C$, corresponding to the experimental manipulations $A$ and ~$A$.

I would like to say that $A$ causes an increase in $B$, and increases in $B$ lead to an increase in $C$. $A$ should lead to increases in $C$, if and only if it leads to increases in $B$ (full mediation).

Paired t-tests confirm $B$ is higher for $A$ vs ~$A$, and $C$ is higher for $A$ vs ~$A$. $\Delta B$ is highly correlated with $\Delta C$. I'm relying on difference scores under the assumption that $B$ and $C$ are not necessarily correlated because of individual differences in the baseline of $B$.

How can I test for mediation here? Since $A$ is binary, there is no "$\Delta A$" with which to run a regression analysis. I'm not sure where to go next; any help is appreciated!

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I believe you will want to take the "counterfactual" approach. Here is a recent paper of possible interest: Imai, Keele, and Tingley (2010). "A General Approach to Causal Mediation Analysis". Psychological Methods, 15:4, 309-334. Link to paper. – Jason Morgan Aug 3 '12 at 23:23